Improving the accuracy and consistency of the energy quadratization method with an energy-optimized technique

We propose an energy-optimized invariant energy quadratization method to solve the gradient flow models in this paper, which requires only one linear energy-optimized step to correct the auxiliary variables on each time step. In addition to inheriting the benefits of the baseline and relaxed invariant energy quadratization method, our approach has several other advantages. Firstly, in the process of correcting auxiliary variables, we can directly solve linear programming problem by the energy-optimized technique, which greatly simplifies the nonlinear optimization problem in the previous relaxed invariant energy quadratization method. Secondly, we construct new linear unconditionally energy stable schemes by applying backward Euler formulas and Crank-Nicolson formula, so that the accuracy in time can reach the first- and second-order. Thirdly, comparing with relaxation technique, the modified energy obtained by energy-optimized technique is closer to the original energy, meanwhile the accuracy and consistency of the numerical solutions can be improved. Ample numerical examples have been presented to demonstrate the accuracy, efficiency and energy stability of the proposed schemes.Comment: 35 pages, 39 figure

Structure−Function Correlation of Chloroquine and Analogues as Transgene Expression Enhancers in Nonviral Gene Delivery

To understand how chloroquine (CQ) enhances transgene expression in polycation-based, nonviral gene delivery systems, a number of CQ analogues with variations in the aliphatic amino side chain or in the aromatic ring are synthesized and investigated. Our studies indicate that the aliphatic amino moiety of CQ is essential to provide increased gene expression. Further, the enhancements are more dramatically affected by changes to the aromatic ring and are positively correlated to the strength of intercalation between DNA and the CQ analogues. Quinacrine (QC), a CQ analogue with a fused acridinyl structure that can strongly intercalate DNA, enhances transfection similarly to CQ at a concentration 10 times lower, while N^4-(4-pyridinyl)-N^1,N^1-diethyl-1,4-pentanediamine (CP), a CQ analogue that has a weakly intercalating pyridinyl ring, shows no effect on gene expression. Subtle change on the 7-substituent of the chloroquine aromatic structure can also greatly affect the ability of the CQ analogues to enhance transgene expression. Transfection in the presence of N^4-(7-trifluoromethyl-4-quinolinyl)-N^1,N^1-diethyl-1,4-pentanediamin e (CQ7a) shows expression efficiency 10 times higher than in the presence of CQ at same concentration, while transfection in the presence of N^4-(4-quinolinyl)-N^1,N^1-diethyl-1,4-pentanediamine (CQ7b) does not reveal any enhancing effects on expression. Through a number of comparative studies with CQ and its analogues, we conclude that there are at least three mechanistic features of CQ that lead to the enhancement in gene expression:  (i) pH buffering in endocytic vesicles, (ii) displacement of polycations from the nucleic acids in polyplexes, and (iii) alteration of the biophysical properties of the released nucleic acid

A Critical Escape Probability Formulation for Enhancing the Transient Stability of Power Systems with System Parameter Design

For the enhancement of the transient stability of power systems, the key is to define a quantitative optimization formulation with system parameters as decision variables. In this paper, we model the disturbances by Gaussian noise and define a metric named Critical Escape Probability (CREP) based on the invariant probability measure of a linearised stochastic processes. CREP characterizes the probability of the state escaping from a critical set. CREP involves all the system parameters and reflects the size of the basin of attraction of the nonlinear systems. An optimization framework that minimizes CREP with the system parameters as decision variablesis is presented. Simulations show that the mean first hitting time when the state hits the boundary of the critical set, that is often used to describe the stability of nonlinear systems, is dramatically increased by minimizing CREP. This indicates that the transient stability of the system is effectively enhanced. It also shown that suppressing the state fluctuations only is insufficient for enhancing the transient stability. In addition, the famous Braess' paradox which also exists in power systems is revisited. Surprisingly, it turned out that the paradoxes identified by the traditional metric may not exist according to CREP. This new metric opens a new avenue for the transient stability analysis of future power systems integrated with large amounts of renewable energy.Comment: 15 pages, 4 figures, 2 table

Control of the Power Flows of a Stochastic Power System

How to determine the power supply of a power system to guarantee that the state remains during a short horizon in a critical subset of the state set? The critical subset is related to the power flows of all power lines of a power system and to transient stability. The control objective is to minimize a cost function. That function is defined as the maximal power flow over all power lines, including a multiple of its standard deviation, as a function of the power supply vector. That the controlled system has an improved performance is shown by numerical results of three academic examples including an eight-node academic network, a twelve-node ring network, and a Manhattan-grid network.Comment: A supplement with 20 pages, 5 figures, 43 tables has been added to the original manuscrip

Evaluating the safety and efficiency of day-care hysterectomy: a comparative study using propensity score matching

ObjectiveTo compare the outcomes of hysterectomy performed via traditional inpatient procedure versus day-care procedure with a focus on surgical time, post-operative recovery, costs, and patient satisfaction, using propensity score matching (PSM) to adjust for confounding variables.MethodsA total of 519 patients undergoing hysterectomy were initially identified. After PSM, 340 patients were included for analysis. Primary outcomes included perioperative complications, surgical time, post-operative discomfort, hospital stay, total cost, and patient satisfaction. Multiple linear regression analysis was performed to explore factors associated with operative bleeding and surgical time. Binary logistic regression was employed to analyze the factors influencing postoperative discomfort.ResultsAfter PSM, the day-care group demonstrated significantly lower hemoglobin decline, post-operative discomfort rates, hospital stay, and total cost, along with higher patient satisfaction (p < 0.05). Multivariate analysis showed a significant correlation between post-operative discomfort and both surgical modality and procedure time. For each additional minute of surgery time, the risk of post-operative discomfort increased by 2% (95% CI: 1.01, 1.03, p < 0.001). Furthermore, the ERAS-based day-care surgical modality reduced the risk of post-operative discomfort by 80% (95% CI: 0.08, 0.50, p < 0.001).ConclusionThe day-care procedure, guided by an enhanced recovery after surgery protocol, not only reduces hospital stay and overall costs but also improves patient satisfaction and reduces post-operative complications without compromising safety. These findings support the feasibility and benefits of day-care hysterectomy as a viable option for appropriately selected patients, offering significant advantages in terms of recovery and cost-efficiency

Controlled synthesis of monodisperse gold nanorods with different aspect ratios in the presence of aromatic additives

This paper reports the synthesis of monodisperse gold nanorods (GNRs) via a simple seeded growth approach in the presence of different aromatic additives, such as 7-bromo-3-hydroxy-2-naphthoic acid (7-BrHNA), 3-hydroxy-2-naphthoic acid (HNA), 5-bromosalicylic acid (5-BrSA), salicylic acid (SA) or phenol (PhOH). Effects of the aromatic additives and hydrochloric acid (HCl) on the structure and optical properties of the synthesized GNRs were investigated. The longitudinal surface plasmon resonance (LSPR) peak wavelength of the resulting GNRs was found to be dependent on the aromatic additive in the following sequence: 5-BrSA (778 nm) > 7-BrHNA (706 nm) > SA (688 nm) > HNA (676 nm) > PhOH (638 nm) without addition of HCl, but this was changed to 7-BrHNA (920 nm) > SA (890 nm) > HNA (872 nm) > PhOH (858 nm) > 5-BrSA (816 nm) or 7-BrHNA (1005 nm) > PhOH (995 nm) > SA (990 nm) > HNA (980 nm) > 5-BrSA (815 nm) with the addition of HCl or HNO3 respectively. The LSPR peak wavelength was increased with the increasing concentration of 7-BrHNA without HCl addition, however, there was a maximum LSPR peak wavelength when HCl was added. Interestingly, the LSPR peak wavelength was also increased with amount of HCl added. The results presented here thus established a simple approach to synthesize monodisperse GNRs of different LSPR wavelength

A Fast Finite Difference Method for 2D Time Fractional Mobile/Immobile Equation with Weakly Singular Solution

This paper presents a fast Crank–Nicolson L1 finite difference scheme for the two-dimensional time fractional mobile/immobile diffusion equation with weakly singular solution at the initial moment. First, the time fractional derivative is discretized using the Crank–Nicolson formula on uniform meshes, and a local truncation error estimate is provided. The spatial derivative is discretized using the central difference quotient on uniform meshes. Then, energy analysis methods are utilized to provide an optimal error estimates. On the other hand, the numerical scheme is optimized based on the sum-of-exponentials approximation, effectively reducing computation and memory requirements. Finally, numerical examples are simulated to verify the effectiveness of the algorithm